Go out to the Lakewalk area and grab coffee at POV. It is a great spot and that whole little area with the lake, the Stella, the few shops, etc. will leave a nice impression. If it is nice weather walk around the lake and go up in the observation deck.

I think the great thing about B/CS these days is that there are multiple "scenes" depending on what you're into. There's no 'best way' to show off the area because there are enough options that it really depends on what the person is into.

Take her downtown - there's a great coffee shop, bars for people past undergrad age, lots of locally owned restaurants, a farmers market on Saturday mornings, a couple of live music venues, lots of little shops, even a full fledged chocolatier.